Corrections and clarifications

There is an error in Figure 3.3. This is the tree diagram representing Eddy's (1982) medical problem. For the branch representing P(Negative | Cancer) the probability should be 0.208, NOT 0.028. Accordingly, the number at the rightmost end of the branch should be 0.0028, NOT 0.00028.

This does not affect the answer to the problem stated in the text, which remains 0.077.

My thanks to Chloe Turner (one of my students) for pointing this out.

Thursday, 4 June 2009

The public's probabilistic numeracy

In the 1960s some psychologists formed the view that people were "intuitive statisticians", but in the 1970s this gave way to a new view of people as "irrational" due to their apparent reliance on heuristics. Hertwig et al (2008) have pointed out that these views were formed on the basis of different types of task. The earlier types of task tended to be "pure applications of probability theory", such as the following: "You toss two coins. What is the probability that both coins come up heads on this toss?" By contrast, the latter problems were more everyday types of task, such as the Linda problem discussed in the previous blog.

Hertwig et al also noted that participants in probabilistic reasoning studies are typically university students. They conducted a telephone survey of 1000 adults in Switzerland, whose numbers had been randomly selected by computer. Each person was presented with four "pure" probability problems and two "everyday" probability problems. As expected, they found a higher level of performance on the pure problems. Moreover, on these problems higher levels of educational achievement were associated with higher levels of reasoning performance.

On the everyday problems, there was actually a tendency towards poorer performance by the most highly educated respondents. This appears to be inconsistent with previous research in which the SAT scores of the American participants were recorded.

Finally, people with some gambling experience also showed a slight performance advantage, as did male participants relative to women.

The study does appear to assume that education is a causal factor in producing correct probabilistic responses on the pure problems. However, the study does not actually distinguish between the cognitive ability of the respondents and their education; or to put it another way, those with higher cognitive ability are more likely to go on to higher levels of education in the first place. Likewise, does gambling experience confer a better understanding of probabilitistic problems, or is it just that people with better understanding are more likely to gamble?


Hertwig, R., Zangerl, M.A., Biedert, E., and Margraf, J. (2008). The public's probabilistic numeracy: How tasks, education and exposure to games of chance shape it. Journal of Behavioral Decision Making, 21 (4), 457-470.

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